The drag-reducing potential of superhydrophobic surfaces (SHSs) may be compromised by trace amounts of surfactant [1]}.
In this paper, we have derived a systematic asymptotic theory for 3D laminar flow, in a plane periodic channel with SHSs along both walls, which has been contaminated with soluble surfactant.
The mass, momentum and surfactant equations are solved in the Stokes flow limit, where the adsorption–desorption kinetics and equation of state are linearised.
We have investigated regimes where cross-channel concentration gradients are small, developing a long-wave theory that accounts for a rapidly equilibrating surfactant-driven transverse flow.
This results in a one-dimensional model (REF )–(REF ) for surfactant transport, which incorporates advection, diffusion, Marangoni effects and exchange between the bulk and the interface.
Using this theory, we gain access to parts of the parameter space that is unavailable using models that assume uniform shear stress at the interface [2]}, [3]}, and we make asymptotic predictions that complement and agree with expensive numerical simulations of the 3D fluid and surfactant equations [4]}.
